Products related to Theory:
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Information and Coding Theory
As this Preface is being written, the twentieth century is coming to an end.Historians may perhaps come to refer to it as the century of information, just as its predecessor is associated with the process of industrialisation.Successive technological developments such as the telephone, radio, television, computers and the Internet have had profound effects on the way we live.We can see pic tures of the surface of Mars or the early shape of the Universe.The contents of a whole shelf-load of library books can be compressed onto an almost weight less piece of plastic.Billions of people can watch the same football match, or can keep in instant touch with friends around the world without leaving home.In short, massive amounts of information can now be stored, transmitted and processed, with surprising speed, accuracy and economy.Of course, these developments do not happen without some theoretical ba sis, and as is so often the case, much of this is provided by mathematics.Many of the first mathematical advances in this area were made in the mid-twentieth century by engineers, often relying on intuition and experience rather than a deep theoretical knowledge to lead them to their discoveries.Soon the math ematicians, delighted to see new applications for their subject, joined in and developed the engineers' practical examples into wide-ranging theories, com plete with definitions, theorems and proofs.
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Algebraic Coding Theory (Revised Edition)
This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm.Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems.Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two.Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.
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Introduction To Algebraic Coding Theory
We live in the age of technology where messages are transmitted in sequences of 0's and 1's through space.It is possible to make an error with noisy channels, so self-correcting codes become vital to eradicate all errors (as the number of errors is small).These self-correcting codes are widely used in the industry for a variety of applications including e-mail, telephone, remote sensing (e.g., photographs of Mars), amongst others.We will present some essentials of the theory in this book.Using linear algebra, we have the salient Hamming codes.The next level of coding theory is through the usage of ring theory, especially polynomials, rational functions and power series, to produce BCH codes, Reed-Solomon codes and the classical Goppa codes.Then we progress to the geometric Goppa code using Algebraic Geometry.
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Concise Encyclopedia of Coding Theory
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon.Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance boundsPart II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphsPart III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
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What is the difference between web development and software development?
Web development primarily focuses on creating websites and web applications that are accessed through a web browser, using technologies such as HTML, CSS, and JavaScript. Software development, on the other hand, involves creating applications that can run on various platforms, including desktop computers, mobile devices, and servers. While web development is a subset of software development, software development encompasses a broader range of applications beyond just web-based ones.
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What training opportunities are available for IT specialists to specialize in web development and general programming, such as software development?
There are various training opportunities available for IT specialists looking to specialize in web development and general programming. Online platforms like Coursera, Udemy, and Codecademy offer courses and certifications in programming languages such as Python, Java, and JavaScript. Additionally, coding bootcamps like General Assembly and Flatiron School provide intensive, hands-on training in software development. IT specialists can also pursue advanced degrees in computer science or related fields to deepen their knowledge and skills in web development and programming.
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What training options are available for IT specialists to specialize in web development and general programming, such as software development?
IT specialists looking to specialize in web development and general programming have a variety of training options available to them. They can pursue formal education through degree programs in computer science or related fields, attend coding bootcamps that offer intensive training in programming languages and frameworks, or take online courses and tutorials to learn specific skills. Additionally, IT specialists can participate in workshops, seminars, and conferences to stay updated on the latest trends and technologies in web development and software development. Continuous learning and practice are essential for IT specialists to excel in these specialized areas.
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Is learning programming and software development very challenging?
Learning programming and software development can be challenging for some people, as it requires logical thinking, problem-solving skills, and attention to detail. However, with dedication, practice, and the right resources, it is definitely achievable. Breaking down complex concepts into smaller, more manageable parts and seeking help from online tutorials, courses, and communities can make the learning process easier and more enjoyable. Ultimately, the level of challenge will vary depending on the individual's background, experience, and learning style.
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Development of Social Theory
Originally published in 1924, Development of Social Theory was written to expand on an outline of the subject in order to turn it into a year’s course of graduate study.From Plato to the writers and teachers of the time, it presents the theorists themselves, giving a historic background, followed by their theory and its subsequent development.It was highly regarded, and widely used as a text for many years.Today it can be read in its historical context.
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Information Theory : From Coding to Learning
This enthusiastic introduction to the fundamentals of information theory builds from classical Shannon theory through to modern applications in statistical learning, equipping students with a uniquely well-rounded and rigorous foundation for further study.Introduces core topics such as data compression, channel coding, and rate-distortion theory using a unique finite block-length approach.With over 210 end-of-part exercises and numerous examples, students are introduced to contemporary applications in statistics, machine learning and modern communication theory.This textbook presents information-theoretic methods with applications in statistical learning and computer science, such as f-divergences, PAC Bayes and variational principle, Kolmogorov's metric entropy, strong data processing inequalities, and entropic upper bounds for statistical estimation.Accompanied by a solutions manual for instructors, and additional standalone chapters on more specialized topics in information theory, this is the ideal introductory textbook for senior undergraduate and graduate students in electrical engineering, statistics, and computer science.
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Stochastic Control Theory : Dynamic Programming Principle
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons.Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory.When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise.This problem is treated in the same frameworks, via the nonlinear semigroup.Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise).Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation.The existence and uniqueness of solutions and regularities as well as Itô's formula are stated.A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space.The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with.Here, for finite time-horizon control problems, DPP was formulated as aone-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method.The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes.Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.
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Nonlinear Programming : Theory and Algorithms (Set)
Presenting recent developments of key topics in nonlinear programming, this text looks specifically at three main areas; convex analysis, optimality conditions and dual computational techniques.
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Which programming languages are used in software development?
There are many programming languages used in software development, including popular languages such as Java, Python, C++, JavaScript, and Ruby. Each language has its own strengths and is used for different purposes in software development. For example, Java is commonly used for building enterprise-level applications, while Python is known for its simplicity and versatility. C++ is often used for system software and game development, while JavaScript is essential for web development. Overall, the choice of programming language depends on the specific requirements of the software being developed.
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What is the difference between software development and programming?
Software development is a broader term that encompasses the entire process of creating software, including planning, designing, testing, and maintaining software applications. Programming, on the other hand, refers specifically to the act of writing code to instruct a computer to perform certain tasks. While programming is a key component of software development, software development involves a more comprehensive approach that includes various stages beyond just writing code.
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Which programming language should a beginner learn if they aim for a well-rounded and software web development?
A beginner aiming for a well-rounded understanding of software and web development should consider learning JavaScript. JavaScript is a versatile language that is used for both front-end and back-end development, making it a valuable skill for web development. Additionally, JavaScript has a large and active community, plenty of resources for learning, and is widely used in the industry. Learning JavaScript will provide a strong foundation for understanding programming concepts and will open up opportunities for a career in software and web development.
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Which programming language do you think is best for web development?
The best programming language for web development depends on the specific requirements of the project and the developer's expertise. However, some popular languages for web development include JavaScript, Python, and Ruby. JavaScript is commonly used for front-end development, while Python and Ruby are often used for back-end development. Ultimately, the best programming language for web development is one that the developer is comfortable with and that best suits the project's needs.
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